The problem of quantifying uncertainty has not been well solved. To
measure the uncertainty of uncertain variables, we first propose the
concept of arc entropy via uncertainty distributions and introduce a new
effective method in this paper. Some properties of arc entropy are
derived, and some practical examples of uncertain variables are given. A
formula for arc entropy is derived via inverse uncertainty
distributions, and several basic theorems are proposed. Moreover, two
general arc entropies are defined, and their properties are
investigated. An application to uncertain learning curves is introduced,
and an uncertain learning curve model is proposed. Another application
to portfolio selection is presented, and its mathematical model is
established.